2. Aggregation across goods Why local analysis is rational? That is, it's rational to model consumer choice by partial maximization What's the restriction of the preference that we can do like that Separability: partitioning consumption bundle into two“sub- bundles”.(x,z)and price vector(p, g)
2.Aggregation across goods • Why local analysis is rational? That is, it’s rational to model consumer choice by partial maximization. • What’s the restriction of the preference that we can do like that. • Separability: partitioning consumption bundle into two “sub-bundles”. (x, z) and price vector (p, q)
2. Aggregation across goods UMP: max u(x, z) S.t. px+ gz=w Let p=f(p),x=g(x) and set max U(x, z) S.t. px t qz=w Solution x(p, q, w)=g(x'(p, q, w), how can we get it
2.Aggregation across goods • UMP: • Let: and set: • Solution ,how can we get it. max ( ) . . u s t w + = x,z px qz p f x g = = ( ), ( ) p x max ( ) . . x U x s t px w + = , z , z qz x p w g w ( , , ) ( ( , , )) q x p q =